Write the equation of a line that is parallel to ${y=\dfrac{1}{2}x-4}$ and that passes through the point ${(9,-6)}$.
Solution: Getting started Key idea: Parallel lines have the same slope. Step 1: Find the slope Slope of the given line: ${\dfrac{1}{2}}$ Slope of the parallel line: $C{\dfrac{1}{2}}$ Step 2: Substitute the known point into linear equation The parallel line will have a slope of $C{\dfrac{1}{2}}$ and pass through the point ${(9,-6)}$. Let's start from the point-slope form of the equation of the parallel line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{(-6)} &= C{\dfrac{1}{2}}(x-{9})\\\\\\ y+6 &= C{\dfrac{1}{2}}x -\dfrac{9}{2} \\\\\\ y &= C{\dfrac{1}{2}}x {-\dfrac{21}{2}} \end{aligned}$ Answer The equation of the parallel line is $y = C{\dfrac{1}{2}}x {-\dfrac{21}{2}}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${\llap{-}10}$ ${\llap{-}12}$ ${\llap{-}14}$ $y$ $x$